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Creators/Authors contains: "Hacon, Christopher D"

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  1. ; (, Science China Mathematics)
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  2. ; (, Cambridge Journal of Mathematics)
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  3. ; (, Bollettino dell'Unione Matematica Italiana)
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  4. ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract In this paper we prove a result on the effective generation of pluri-canonical linear systems on foliated surfaces of general type. Fix a function {P:\mathbb{Z}_{\geq 0}\to\mathbb{Z}} , then there exists an integer {N>0} such that if {(X,{\mathcal{F}})} is a canonical or nef model of a foliation of general type with Hilbert polynomial {\chi(X,{\mathcal{O}}_{X}(mK_{\mathcal{F}}))=P(m)} for all {m\in\mathbb{Z}_{\geq 0}} , then {|mK_{\mathcal{F}}|} defines a birational map for all {m\geq N} . On the way, we also prove a Grauert–Riemenschneider-type vanishing theorem for foliated surfaces with canonical singularities. 
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